Investigation on modulation of multi-frequency ultrasonic waves in structures with quadratic nonlinearity

In this study, the modulation of multiple frequency content of a single ultrasonic wave in nonlinear structures is investigated analytically, numerically and experimentally. An experimental technique is proposed based on nonlinear lamb wave propagation in aluminum bars using piezoelectric wafer active sensors (PWAS) to study intrinsic nonlinearity of structures. First, a one-dimensional analytical procedure is developed to study the modulation of one dimensional wave with multiple-frequency content in isotropic medium with quadratic nonlinearity. This procedure is implemented to study modulation of frequency contents of a well-known tone burst signal in nonlinear medium. Then, predictions obtained by the proposed analytical procedure are compared with the results of finite element model, which show strong correlations. The experimental and analytical results reveal that in excitation with a train of tone burst, due to frequency modulation, some new harmonics including a strong sub harmonic generation with frequency of f0/Np appear in the response. The amplitude of this harmonic is even higher than common second harmonic generation (2f0). This can be seen in the experimental results when the excitation frequencies are correctly selected. Finally, it is explained that, why the new sub harmonic generation is less affected by the nonlinearity induced by the excitation system.